Let X1,..., Xn be iid n(, a2), where a is a known constant and > 0.

Question:

Let X1,..., Xn be iid n(θ, aθ2), where a is a known constant and θ > 0.
a. Show that the parameter space does not contain a two-dimensional open set.
b. Show that the statistic T = (, S2) is a sufficient statistic for θ, but the family of distributions is not complete.